Label
Class
Class size
Class degree
Base field
Field degree
Field signature
Conductor
Conductor norm
Discriminant norm
Root analytic conductor
Bad primes
Rank
Torsion
CM
CM
Sato-Tate
$\Q$-curve
Base change
Semistable
Potentially good
Nonmax $\ell$
mod-$\ell$ images
$Ш_{\textrm{an}}$
Tamagawa
Regulator
Period
Leading coeff
j-invariant
Weierstrass coefficients
Weierstrass equation
41.1-a1
41.1-a
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
41.1
\( 41 \)
\( 41 \)
$0.50561$
$(a+6)$
0
$\Z/7\Z$
$\textsf{no}$
$\mathrm{SU}(2)$
✓
$7$
7B.1.1
$1$
\( 1 \)
$1$
$46.26087846$
0.422214159
\( -\frac{176128}{41} a - \frac{110592}{41} \)
\( \bigl[0\) , \( -\phi\) , \( \phi\) , \( 0\) , \( 0\bigr] \)
${y}^2+\phi{y}={x}^{3}-\phi{x}^{2}$
1025.1-a1
1025.1-a
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
1025.1
\( 5^{2} \cdot 41 \)
\( 5^{6} \cdot 41 \)
$1.13059$
$(-2a+1), (a+6)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1
$1$
\( 1 \)
$1$
$3.626679053$
1.621900179
\( -\frac{176128}{41} a - \frac{110592}{41} \)
\( \bigl[0\) , \( -\phi - 1\) , \( \phi\) , \( \phi - 1\) , \( 2 \phi - 4\bigr] \)
${y}^2+\phi{y}={x}^{3}+\left(-\phi-1\right){x}^{2}+\left(\phi-1\right){x}+2\phi-4$
1681.3-b1
1681.3-b
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
1681.3
\( 41^{2} \)
\( 41^{7} \)
$1.27943$
$(a+6)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1
$1$
\( 2 \)
$1$
$1.266491262$
1.132784221
\( -\frac{176128}{41} a - \frac{110592}{41} \)
\( \bigl[0\) , \( 1\) , \( \phi\) , \( 8 \phi - 20\) , \( 140 \phi - 238\bigr] \)
${y}^2+\phi{y}={x}^{3}+{x}^{2}+\left(8\phi-20\right){x}+140\phi-238$
3321.1-f1
3321.1-f
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
3321.1
\( 3^{4} \cdot 41 \)
\( 3^{12} \cdot 41 \)
$1.51684$
$(a+6), (3)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1
$1$
\( 2 \)
$0.432983079$
$2.703166965$
2.093720884
\( -\frac{176128}{41} a - \frac{110592}{41} \)
\( \bigl[0\) , \( 0\) , \( \phi\) , \( -3 \phi - 3\) , \( -3 \phi - 5\bigr] \)
${y}^2+\phi{y}={x}^{3}+\left(-3\phi-3\right){x}-3\phi-5$
4961.4-f1
4961.4-f
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
4961.4
\( 11^{2} \cdot 41 \)
\( 11^{6} \cdot 41 \)
$1.67693$
$(-3a+2), (a+6)$
$1$
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1
$1$
\( 2 \)
$0.235455977$
$7.196950528$
3.031330060
\( -\frac{176128}{41} a - \frac{110592}{41} \)
\( \bigl[0\) , \( -\phi\) , \( \phi\) , \( -2 \phi - 3\) , \( 8 \phi - 2\bigr] \)
${y}^2+\phi{y}={x}^{3}-\phi{x}^{2}+\left(-2\phi-3\right){x}+8\phi-2$
4961.6-e1
4961.6-e
$2$
$7$
\(\Q(\sqrt{5}) \)
$2$
$[2, 0]$
4961.6
\( 11^{2} \cdot 41 \)
\( 11^{6} \cdot 41 \)
$1.67693$
$(-3a+1), (a+6)$
0
$\mathsf{trivial}$
$\textsf{no}$
$\mathrm{SU}(2)$
$7$
7B.6.1
$1$
\( 1 \)
$1$
$4.738782752$
2.119248073
\( -\frac{176128}{41} a - \frac{110592}{41} \)
\( \bigl[0\) , \( -\phi\) , \( \phi\) , \( -5 \phi - 4\) , \( -7 \phi - 2\bigr] \)
${y}^2+\phi{y}={x}^{3}-\phi{x}^{2}+\left(-5\phi-4\right){x}-7\phi-2$
Download
displayed columns for
results
to
Text
Pari/GP
SageMath
Magma
Oscar
CSV
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.